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The Unique-lowest Sealed-bid Auction

Author

Listed:
  • Harold Houba

    () (VU University Amsterdam)

  • Dinard van der Laan

    () (VU University Amsterdam)

  • Dirk Veldhuizen

    () (VU University Amsterdam)

Abstract

This discussion paper resulted in a publication in 'Theory and Decision' , 2011, 71(2), 269-295. Unique-lowest sealed-bid auctions are auctions in which participation is endogenous and the winning bid is the lowest bid among all unique bids. Such auctions admit very many Nash equilibria (NEs) in pure and mixed strategies. The two-bidders' auction is similar to the Hawk-Dove game, which motivates to study symmetric NEs: Properties and comparative statics are derived and the symmetric NE with the lowest expected gains is the maximin in symmetric strategies, which allows computation through a mathematical program. Simulations provide numerical evidence that the symmetric NE with the lowest expected gains is the unique limit point of the replicator dynamics.

Suggested Citation

  • Harold Houba & Dinard van der Laan & Dirk Veldhuizen, 2008. "The Unique-lowest Sealed-bid Auction," Tinbergen Institute Discussion Papers 08-049/1, Tinbergen Institute.
  • Handle: RePEc:tin:wpaper:20080049
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    File URL: http://papers.tinbergen.nl/08049.pdf
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    References listed on IDEAS

    as
    1. Jürgen Eichberger & Dmitri Vinogradov, 2008. "Least Unmatched Price Auctions: A First Approach," Working Papers 0471, University of Heidelberg, Department of Economics, revised Jul 2008.
    2. Roger B. Myerson, 1998. "Population uncertainty and Poisson games," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(3), pages 375-392.
    3. Myerson, Roger B., 2000. "Large Poisson Games," Journal of Economic Theory, Elsevier, vol. 94(1), pages 7-45, September.
    4. Becker, Johannes Gerd & Damianov, Damian S., 2006. "On the existence of symmetric mixed strategy equilibria," Economics Letters, Elsevier, vol. 90(1), pages 84-87, January.
    5. Maciej Bukowski & Jacek Miekisz, 2004. "Evolutionary and asymptotic stability in symmetric multi-player games," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(1), pages 41-54, January.
    6. Rapoport, Amnon & Otsubo, Hironori & Kim, Bora & Stein, William E., 2007. "Unique bid auctions: Equilibrium solutions and experimental evidence," MPRA Paper 4185, University Library of Munich, Germany, revised 17 Jul 2007.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Di Gaetano, Luigi, 2011. "A model of descending auction with hidden starting price and endogenous price decrease," MPRA Paper 35773, University Library of Munich, Germany.
    2. Marco Scarsini & Eilon Solan & Nicolas Vieille, 2010. "Lowest Unique Bid Auctions," Papers 1007.4264, arXiv.org.

    More about this item

    Keywords

    Auctions; Sealed-Bid Auction; Evolutionary Stability; Endogenous Entry; Maximin;

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • L83 - Industrial Organization - - Industry Studies: Services - - - Sports; Gambling; Restaurants; Recreation; Tourism

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